One-Step Suicide Substrate Inactivation Kinetics of a Ping-Pong Reaction with One Substrate Undergoing Disproportionation: A Theoretical Approach with Approximate Solutions

Abstract

Understanding the kinetic mechanism of enzyme inactivation by suicide substrate is of relevance for the optimal design of new drugs with pharmacological and therapeutic applications. Suicide substrate inactivation usually occurs via a two-step mechanism, although there are enzymes such as peroxidase and catalase in which the suicide inactivation by H2O2 happens in a single step. The approximate solution of the ordinary differential equation (ODE) system of the one step suicide substrate inactivation kinetics for a uni–uni reaction following the irreversible Michaelis–Menten model was previously analytically solved when accumulation of the substrate–enzyme complex was negligible, however not for more complex models, such as a ping-pong reaction, in which the enzyme is present in two active states during the catalytic turnover. To solve this issue, a theoretical approach was followed, in which the standard quasi-steady state and reactant stationary approximations were invoked. These approximations allowed for solving the ODE system of a ping-pong reaction with one substrate undergoing disproportionation when suicide inactivation was also present. Although the approximate analytical solutions were rather unwieldy, they were still valuable in qualitative analyses to explore the time course of the reaction products and identify the enzyme active state that irreversibly reacted with the suicide substrate during the reaction.